Method of coordinating concurrent sector optimizations in a wireless communication system

ABSTRACT

Embodiments of the claimed subject matter provide a method and apparatus for coordinating concurrent sector optimizations in a wireless communication system. One exemplary embodiment of the method includes determining neighbor relationships between sectors and constructing a precedence graph using the neighbor relationships to link neighboring sectors by a plurality of directed arcs to indicate relative precedence of the neighboring sectors. The exemplary embodiment the method also includes iteratively allocating one or more antenna resources of each of the sectors by selecting a subset of the sectors as master sectors, concurrently optimizing allocation of the antenna resource for each master sector and its associated slave sectors, and reversing precedence indicated by the directed arcs linked to each master sector following optimization of the allocation of the antenna resource(s).

BACKGROUND

This application relates generally to communication systems, and, moreparticularly, to wireless communication systems.

Wireless communication systems typically deploy numerous base stations(or other types of wireless access points such as eNodeBs) for providingwireless connectivity to user equipment such as mobile units or otherwireless-enabled devices. Each base station is responsible for providingwireless connectivity to the user equipment located in a particular cellor sector served by the base station. The air interface between the basestation and the user equipment supports downlink (or forward link)channels for carrying information from the base station to the userequipment and uplink (or reverse link) channels for carrying informationfrom the user equipment to the base station. The uplink and/or downlinkchannels typically include data channels for carrying data traffic suchas voice information and control channels for carrying control signalsuch as pilot signals, synchronization signals, acknowledgment signals,and the like.

Conventional base stations may use antennas or arrays of antennas thatcan be reconfigured after deployment. For example, parameters such asthe antenna tilt, azimuth, transmission power, or beamwidth can bevaried to modify the coverage area of the antenna or antenna array. Thetypical approach for reconfiguring base station antennas uses drive-bytesting to evaluate the coverage provided by a network of base stationsand then manually reconfiguring the base station antennas to modify thecoverage area based upon the results of the drive-by testing. However,manual intervention is typically very costly, which limits itsapplicability.

SUMMARY OF EMBODIMENTS

The disclosed subject matter is directed to addressing the effects ofone or more of the problems set forth above. The following presents asimplified summary of the disclosed subject matter in order to provide abasic understanding of some aspects of the disclosed subject matter.This summary is not an exhaustive overview of the disclosed subjectmatter. It is not intended to identify key or critical elements of thedisclosed subject matter or to delineate the scope of the disclosedsubject matter. Its sole purpose is to present some concepts in asimplified form as a prelude to the more detailed description that isdiscussed later.

In one embodiment, a method is provided for coordinating concurrentsector optimization in a wireless communication system. One exemplaryembodiment of the method includes determining neighbor relationshipsbetween sectors and constructing a precedence graph using the neighborrelationships to link neighboring sectors by a plurality of directedarcs to indicate relative precedence of the neighboring sectors. Theexemplary embodiment the method also includes iteratively allocating oneor more antenna resources of each of the sectors by selecting a subsetof the sectors as master sectors, concurrently optimizing allocation ofthe antenna resource for each master sector and its associated slavesectors, and reversing precedence indicated by the directed arcs linkedto each master sector following optimization of the allocation of theantenna resource(s).

In another embodiment, a base station is provided for coordinatingconcurrent sector optimization at the wireless communication system. Oneexemplary embodiment of the base station includes one or more antennas,a transceiver for transmitting and receiving signals via the antennas,and an antenna controller configurable to allocate antenna resources.The antenna controller allocates the antenna resources by determiningwhether a sector served by the base station is a master sector or aslave sector based on a precedence graph that links the sector toneighboring sectors by a plurality of directed arcs to indicate relativeprecedence of the sector and the neighboring sectors. The antennacontroller optimizes allocation of antenna resources of the sector andthe neighboring sectors in response to determining that the sector isthe master sector and receives information indicating allocation ofantenna resources for the sector in response to determining that thesector is the slave sector for one of the neighboring sectors. Theprecedence indicated by the directed arcs is reversed followingoptimization of the allocation of the antenna resources or reception ofthe information indicating allocation of the antenna resources of thesector.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosed subject matter may be understood by reference to thefollowing description taken in conjunction with the accompanyingdrawings, in which like reference numerals identify like elements, andin which:

FIG. 1 conceptually illustrates a first exemplary embodiment of awireless communication system;

FIG. 2A conceptually illustrates a first exemplary embodiment of adistribution of master sectors and associated slave sectors in awireless communication system;

FIG. 2B conceptually illustrates the distribution of master sectors andassociated slave sectors in the wireless communication system shown inFIG. 2A during a different iteration of the optimization procedure;

FIG. 3 conceptually illustrates one exemplary embodiment of a mapping offeatures of the antenna resource allocation technique to thephilosopher's problem;

FIG. 4 conceptually illustrates a second exemplary embodiment of awireless communication system;

FIG. 5 conceptually illustrates one exemplary embodiment of a method forcoordinating concurrent sector optimization at a wireless communicationsystem;

FIG. 6A conceptually illustrates a portion of a precedence graph thatmay be used in embodiments of the techniques described herein;

FIG. 6B conceptually illustrates the portion of a precedence graphfollowing iteration of the optimization process performed on the portiondepicted in FIG. 6A;

FIG. 7 conceptually illustrates one exemplary embodiment of the resultof the simulation that implements embodiments of the sector selectionand optimization process described herein; and

FIG. 8 conceptually illustrates one exemplary embodiment of a server.

While the disclosed subject matter is susceptible to variousmodifications and alternative forms, specific embodiments thereof havebeen shown by way of example in the drawings and are herein described indetail. It should be understood, however, that the description herein ofspecific embodiments is not intended to limit the disclosed subjectmatter to the particular forms disclosed, but on the contrary, theintention is to cover all modifications, equivalents, and alternativesfalling within the scope of the appended claims.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Illustrative embodiments are described below. In the interest ofclarity, not all features of an actual implementation are described inthis specification. It will of course be appreciated that in thedevelopment of any such actual embodiment, numerousimplementation-specific decisions should be made to achieve thedevelopers' specific goals, such as compliance with system-related andbusiness-related constraints, which will vary from one implementation toanother. Moreover, it will be appreciated that such a development effortmight be complex and time-consuming, but would nevertheless be a routineundertaking for those of ordinary skill in the art having the benefit ofthis disclosure. The description and drawings merely illustrate theprinciples of the claimed subject matter. It will thus be appreciatedthat those skilled in the art may be able to devise various arrangementsthat, although not explicitly described or shown herein, embody theprinciples described herein and may be included within the scope of theclaimed subject matter. Furthermore, all examples recited herein areprincipally intended to be for pedagogical purposes to aid the reader inunderstanding the principles of the claimed subject matter and theconcepts contributed by the inventor(s) to furthering the art, and areto be construed as being without limitation to such specifically recitedexamples and conditions.

The disclosed subject matter will now be described with reference to theattached figures. Various structures, systems and devices areschematically depicted in the drawings for purposes of explanation onlyand so as to not obscure the description with details that are wellknown to those skilled in the art. Nevertheless, the attached drawingsare included to describe and explain illustrative examples of thedisclosed subject matter. The words and phrases used herein should beunderstood and interpreted to have a meaning consistent with theunderstanding of those words and phrases by those skilled in therelevant art. No special definition of a term or phrase, i.e., adefinition that is different from the ordinary and customary meaning asunderstood by those skilled in the art, is intended to be implied byconsistent usage of the term or phrase herein. To the extent that a termor phrase is intended to have a special meaning, i.e., a meaning otherthan that understood by skilled artisans, such a special definition willbe expressly set forth in the specification in a definitional mannerthat directly and unequivocally provides the special definition for theterm or phrase. Additionally, the term, “or,” as used herein, refers toa non-exclusive “or,” unless otherwise indicated (e.g., “or else” or “orin the alternative”). Also, the various embodiments described herein arenot necessarily mutually exclusive, as some embodiments can be combinedwith one or more other embodiments to form new embodiments.

A wireless communication system includes numerous base stations thatprovide wireless connectivity (which may also be referred to ascoverage) to a correspondingly large number of sectors. Radiotransmissions from one sector typically interact with or disturb radiotransmissions from neighboring sectors. The interaction of radiotransmissions and the disturbances caused by these interactions may becollectively referred to as interference. The sector coverage or theinterference between neighboring sectors can be optimized by allocatingsector resources such as antenna tilt, azimuth, power, beamwidth, andthe like. For example, the antenna resources of one sector (e.g., themaster sector) can be optimized in conjunction with the antennaresources of neighboring sectors (e.g., one or more slave sectors) thatmay be influenced by changes in the allocation of the antenna resourcesof the master sector. A simple pattern or sequence can be defined sothat each sector has the opportunity to be a master sector during atleast one optimization interval while also acting as a slave sector forother neighboring sectors during other optimization intervals.

Optimizations for groups of master sectors can be performed concurrentlyas long as only one sector at a time is the master sector for aparticular slave sector. Furthermore, the separation between the mastersectors in the predetermined pattern should be selected carefully tomanage the mutual interference between sectors while also making thenumber of master sectors involved in the concurrent optimization aslarge as possible. Interference between the master sectors decreases asthe distance between the master sectors increases. However, if thedistance between the master sectors specified by the predeterminedpattern is too large, then the amount of concurrency is reduced. If thedistance is too small, interference between the master sectors is toolarge and the optimization may be difficult or impossible to perform.The predetermined pattern may balance these competing demands in favorof interference reduction by selecting a relatively large distancebetween the master sectors. However, adopting a relatively largeseparation also reduces the number of optimizations that can beperformed concurrently. Moreover, the separation typically cannot bemodified in response to changes in the performance of the differentsectors, e.g. in response to changes in environmental conditions,interfering obstacles, and the like when the separation is determinedbased on a predetermined range of mutual interference. In someembodiments, extra negotiation and signaling between sectors may be usedto modify the separation(s) on the fly.

At least in part to address these drawbacks in the conventionalpractice, the present application describes embodiments of techniquesfor coordinating concurrent sector optimization of the wirelesscommunication system. In one embodiment, potential master sectors canidentify the neighboring sectors that would act as the slave sectorsduring an optimization performed by each potential master sector. Forexample, a group of sectors can be identified as the slave sectors for aparticular master sector based on the uplink or downlink radiationpattern of the master sector, environmental conditions, interferingobstacles, and the like. Alternatively, neighboring sectors can beidentified using signaling from user equipment that tells the potentialmaster sector which sectors have been detected by user equipment. In oneembodiment, signaling between sectors can also be used to populate theneighbor list with neighbor-of-neighbor information. A directed graphcan then be defined to indicate precedence for each sector to become amaster sector.

Initially, the precedence graph may be defined by assigning differentidentifiers to each sector and then determining the precedence basedupon a comparator such as “greater than.” However, alternativetechniques for breaking the initial symmetry between the sectors mayalso be used. The relative precedence between each pair of sectors canbe indicated by a directed arc that points from the sector with lowerprecedence to the sector with higher precedence. Subsequentprecedence(s) can be determined by reversing the direction of precedenceindicated by the directed are between a master sector and each relatedslave sector in response to the master sector completing an iteration ofthe optimization process. Sectors may be chosen to be master sectorswhen they have precedence over all the neighbor sectors needed for theoptimization and the antenna resources of the selected master sectorsand slave sectors may be concurrently optimized. The packing density ofthe master sectors can be increased by identifying neighboring sectorsusing performance measurements or inter-sector signaling and thenallocating the master/slave sectors for iterations of the optimizationprocess using the precedence graph. Embodiments of the techniquesdescribed herein may therefore significantly increase the concurrency ofthe optimization process and reduce the time required to performiterations. The process can be iterated until each sector has had anopportunity to become the master sector for a selected number ofoptimization intervals.

FIG. 1 conceptually illustrates a first exemplary embodiment of awireless communication system 100. In the illustrated embodiment, thewireless communication system 100 operates according to the standards orprotocols of the Long Term Evolution (LTE) of the standards agreed uponby the Third Generation Partnership Project (3GPP). However, persons ofordinary skill in the art having benefit of the present disclosureshould appreciate that this embodiment is intended to be illustrative.Alternative embodiments of the wireless communication system 100 mayoperate according to other standards, protocols, or combinationsthereof. The wireless communication system 100 includes numerous basestations (not shown in FIG. 1) that are configured to provide wirelessconnectivity to user equipment (not shown in FIG. 1) withincorresponding cells 105. Wireless connectivity is provided usingantennas or antenna arrays associated with the base station. Asdiscussed herein, the antennas or antenna arrays can be configured tooperate using parameters such as an antenna tilt, an azimuth, atransmission power, a beamforming parameter, or a beamwidth. Theseparameters can be modified during operation of the antennas and maytherefore be referred to as dynamic antenna parameters.

In the illustrated embodiment, each cell 105 includes three sectors 110that are served by corresponding antennas or antenna arrays associatedwith the base stations. For example, a base station may include threeantenna arrays and each of the antenna arrays may be used to providecoverage to one of the sectors 110 in the corresponding cell 105. Asused herein, the term “sector” refers to a geographical area served byone or more antennas in the base station. The boundaries of sectors maybe defined by transmission powers of the base station, a beamwidth orangular extent of a radiation pattern defined by the antennaconfiguration, and other factors such as geography, topology, physicalobstructions, and other environmental factors. In some embodiments, theterm “sector” may be synonymous with the term “cell” or (as in theillustrated embodiment) it may refer to a subset of a particular cell105 associated with a base station. In the illustrated embodiment, eachsector 110 is assigned to a sector identifier that identifies the sectorwithin the communication system 100. The cells 105 are depicted in FIG.1 as perfect hexagons and the sectors 110 are depicted as pentagonalportions of the hexagons. However, persons of ordinary skill in the artshould appreciate that the coverage areas of actual cells 105 or sectors110 may be irregular and may change over time, e.g., due to frequency,temporal, or spatial fading caused by geography, topology, physicalobstructions, and other environmental factors.

The neighbor relationships between the sectors 110 may be determinedusing cell planning information, measurements performed by the basestations, measurements performed by user equipment operating in thesectors 110, or other information. In one embodiment, each sector 110has access to existing neighborhood lists provided by the wirelesscommunication system 100, such as a neighbor-of-neighbor-of-neighbor- .. . list that can be built to any depth of neighbor relations. The depthof the neighbor relations list may be chosen based on the mutualinterference levels between one sector and neighbors at the lowest levelof the neighbor relations list. For example, the depth of the neighborrelations list may be limited to neighbors that interfere with a sectorat a level that is above a predetermined threshold.

The levels of mutual interference can be determined using performancemeasurements made by the base stations or user equipment that indicatethe radiation patterns associated with the sectors 110. For example, theradiation pattern for the downlink caused by each base station'semissions may be measured by the user equipment and reported to theirserving base station. The radiation pattern for the uplink caused byuser equipment transmissions may be measured by their serving basestation or neighboring base stations. The mutual interference levels maytherefore be determined without deploying additional equipment orrequiring additional manual testing such as drive tests that measureradiation patterns using detectors in cars that drive through thecoverage area of the wireless communication system 100. Consequently,the radiation patterns, interference levels, or neighbor lists can bedetermined dynamically in response to particular events, atpredetermined time intervals, or substantially continuously to reflectchanging conditions within the wireless communication system 100.

In the illustrated embodiment, the sector 115 (indicated by a bold line)is selected as a master sector and FIG. 1 depicts exemplary neighbors ofthe sector 115. The dashed circle 117 indicates the cells that neighborthe cell including the master sector 115. In one embodiment, performancemeasurements may be used to identify the sectors 120 as immediateneighbor sectors to the sector 115. e.g., because the mutualinterference between the sectors is above a first threshold. Sectors 125may be identified as relevant neighbors-of-neighbors to the sector 115based on mutual interference between the sector 115 and the sectors 125,mutual interference between the sectors 120 and the sectors 125, orother criteria. In the illustrated embodiment, the depth of the neighborlist is three and sectors 130 may be identified as relevantneighbors-of-neighbors-of-neighbor-of-neighbors to the sector 115 basedon mutual interference between combinations of the sectors 115, 120,125, 130. However, persons of ordinary skill in the art having benefitof the present disclosure should appreciate that the depth of theneighbor list may differ from the illustrated embodiment so that thedepth may be larger or smaller than shown in FIG. 1.

The neighbor list may be constructed iteratively in some embodiments. Inone embodiment, the sector 115 may know its direct neighbor sectors 120from measurements performed by user equipment served by the sector 115or the sectors 120. The sectors 115, 120 may therefore be added to theneighbor list. For example, neighbor sectors 120 may be detected by userequipment when the user equipment can receive signaling from sectorsother than the sector that is their current serving sector. Signals fromneighboring sectors can be received by user equipment when the receivedsignal has a minimum signal strength and signal to interference plusnoise ratio (SINR). If the signal strength and interference requirementsare fulfilled, the user equipment can decode the received signals andretrieve information identifying the neighbor sectors. The identifyinginformation or the signal strength may then be reported to the basestation that controls the sector 115 that is serving the user equipment.The sector 115 may then request information from the sectors 120 thatindicates the sectors that are direct neighbors of each sector 120. Inone embodiment, the neighbors-of-neighbors information is retrieved byneighborhood-request signaling between base stations or sectors and thenetwork addresses can be derived from the sector identificationinformation that is reported by the user equipment. Addresses of themore distant neighbors may be contained in the reply that is received bythe sector 120 and this address information can be conveyed to thesector 115. In various embodiments, the communication between thesectors of base stations can be by direct links or via intermediatenodes (acting as routers) if no direct link is established.

The sectors identified by each sector 120 may then be added to theneighbor list. Duplicate sectors that are identified by more than onesector 120 may be removed. The procedure may continue iteratively witheach set of newly added neighbors providing information indicating theirdirect neighbors to the sector 115 so that the newly identifiedneighbors may be added to the neighbor list for the sector 115. Theprocedure may continue until a stop criteria is reached, e.g., after theprocedure has performed a predetermined number of cycles or satisfiedsome other radio dependent criteria such as the mutual interferencebetween the sector 115 and the newly added sectors falling below athreshold.

The neighbor lists for each of the sectors 110 may be used to selectmaster sectors and slave sectors that correspond to the sectorsindicated in the neighbor list for the master sector. The master sectorsoperate as optimization centers for controlling optimization of antennaparameters in the master sector and its associated slave sectors. Forexample, if the sector 115 is selected as a master sector, the sector115 controls optimization of the antenna parameters for the sectors 115,120, 125, 130. Multiple master sectors can perform the optimizationprocedure concurrently as long as the slave sectors for each mastersector are under the control of a single master sector during theconcurrent optimization process. The present application describestechniques for selecting the master sectors in the wirelesscommunication system 100 to attempt to create as much parallelism aspossible by attempting to optimize or maximize the number of mastersectors that can perform the optimization procedure concurrently.Embodiments of the techniques described herein may be able to manage theselection of master sectors in an efficient, distributed, concurrent,and deadlock-free manner including the dynamics of added/removed/failedentities and a dynamically adjustable mutual interference range.

In one embodiment, sectors 110 may be selected as master sectors byconstructing a precedence graph using the neighbor relationships to linkneighboring sectors by directed arcs that indicate relative precedenceof the neighboring sectors. The precedence graph may be initialized byassigning unique or random numbers to each sector 110 and thenestablishing the relative precedence between the sectors 110 usingoperations such as “greater than.” Sectors 110 may be selected as mastersectors when the sector 110 has precedence over its associated slavesectors, which may be identified using the neighbor relationships. Themaster and slave sectors are also determined subject to the constraintthat each slave sector is only associated with one master sector. Oncethe master and slave sectors have been selected, allocation of antennaresources for each master sector and its associated slave sectors may beconcurrently optimized, as discussed herein. The precedence indicated bythe directed arcs linked to each master sector may then be reversed whenthe optimization process for the master sector is complete. The processcan be iterated until a stopping criterion is reached, e.g., until eachof the sectors 110 is selected as a master sector for a predeterminednumber of iterations.

FIG. 2A conceptually illustrates a first exemplary embodiment of adistribution of master sectors and associated slave sectors in awireless communication system 200. In the illustrated embodiment, thesectors 205 are depicted as squares in the interest of clarity. However,persons of ordinary skill in the art having benefit of the presentdisclosure should appreciate that in practice the sectors 205 may haveirregular and possibly time varying shapes. The master sectors areindicated by the circles 210 and have been selected according toembodiments of the techniques described herein. The bold squares 215indicate the neighboring sectors that are under exclusive control of thecorresponding master sector 210 during an iteration of embodiments ofthe optimization procedure described herein. The number of neighboringsectors associated with each master sector 210 can vary, but each slavesector is only associated with one master sector.

FIG. 2B conceptually illustrates the distribution of master sectors andassociated slave sectors in the wireless communication system 200 duringa different iteration of the optimization procedure. In the illustratedembodiment, the master/slave sectors 215 in a previous iteration (asillustrated FIG. 2A) are indicated by dashed boxes in FIG. 2B to providea reference. During the iteration depicted in FIG. 2B a new set ofmaster sectors 220 and their associated slave sectors 225 has beenselected according to embodiments of the techniques described herein.The groups of sectors 215 from the previous iteration overlap in partwith the groups of sectors 225 in the iteration illustrated in FIG. 2B.This overlap may help to speed convergence of the concurrentoptimization procedure, e.g., by reducing the number of iterations thatare required to reach a convergence criteria. For example, overlapbetween the groups of sectors 215, 225 may reduce the number ofiterations that are performed before the fractional change in theoptimized antenna parameters from one iteration to another iterationfalls below a threshold value.

In the illustrated embodiment, substantially all of the sectors 205 maybe optimized. Neighboring sectors mutually interfere with each othersignificantly up to a certain distance or separation between the sectors205. Each of the sectors 205 may therefore be modeled as an independententity that implements that operates an optimization algorithm and alsoincludes antenna resources that are optimized by the sector 205 if it isa master sector or by a neighboring sector if the sector 205 is a slavesector. In one embodiment, the master and slave sectors may be selectedfor concurrent optimization using an algorithm that allows each sector205 to begin to reserve antenna resources of some sectors 205 and itsneighbor list and then if it is successful, the sector 205 may continueto attempt to gain exclusive access to the antenna resources of theother sectors in its neighbor list until it either is granted control ofall the necessary slave sectors or it fails and relinquishes control ofits resources or the resources of its neighbor sectors to another mastersector. However, it is well known that this approach often leads todeadlocks that occur when most of the sectors 205 have been grantedcontrol of the antenna resources of some portion of the sectors in itsneighbor list, but are unable to get the missing ones because these arealready reserved by another sector 205 that is running the samestrategy. None of the sectors 205 can proceed from the deadlock and sothey may wait infinitely.

The present application therefore describes an alternative technique forselecting the master and slave sectors. In one embodiment, the masterand slave sectors may be selected by implementing deadlock avoidancestrategies for resource allocation, which may be referred to assolutions to the philosopher's problem.

FIG. 3 conceptually illustrates one exemplary embodiment of a mapping300 of features of the antenna resource allocation technique to thephilosopher's problem. In the illustrated embodiment, each potentialmaster sector (e.g., each philosopher) is configured to implement anantenna optimization algorithm 305 that may be executed if the potentialmaster sector is able to acquire control of the slave sectors in itsneighbor list. Embodiments of the optimization algorithm 305 arediscussed herein. In the illustrated embodiment, the terms “mastersector” and “antenna optimization algorithm” may be used interchangeablysince each master sector may implement an antenna optimizationalgorithm.

For the philosopher's drinking problem 310, each potential master sectoris able to grant control of its antenna resources 315 or request controlof the antenna resources 315 of other sectors. In the illustratedembodiment, the state of each potential master sector 305 is representedby a state diagram 320. For example, each potential master sector 305may be attempting to acquire control of slave sectors (a trying state),may have granted control of its antenna resources to another mastersector (a hold state), may have already acquired control of the slavesectors and may be performing the optimization procedure (an activestate), may have finished the optimization procedure and be releasingantenna resources (an exit state), or may be idle (an idle state). Thepotential master sectors 305 may also be associated with other variables325 such as a “hold” variable that may be set in response to thepotential master sector 305 transmitting a message that grants controlof its resources to another potential master sector 305, a “request”variable that indicates that the potential master sector 305 hastransmitted a message requesting control of the resources of anotherpotential master sector 305, or other variables.

Each potential master sector 305 may determine whether to grant or denya request for the antenna resources 315 based in part on its currentstate. For example, sectors that are in a trying state may deny requestsfor their resources from sectors that have lower precedence but maygrant requests for the resources from sectors that have higherprecedence. Sectors that are in a hold state because they have alreadygranted control of their antenna resources to another potential mastersector may deny all requests for their antenna resources from othersectors. Sectors that are in an idle state or a free state may grantrequests for control of their antenna resources to other sectorsregardless of their relative precedence. Persons of ordinary skill inthe art having benefit of the present disclosure should appreciate thisembodiment is intended to be illustrative and in alternative embodimentsother rules or policies for granting or denying resource requests may beused.

For the philosopher's dining problem 330, each potential master sectoris able to grant control of its antenna resources 335 or request controlof the antenna resources 335 of another sector. In the illustratedembodiment, the state of each potential master sector 305 is representedby a state diagram 340. For example, each potential master sector 305may be attempting to acquire control of slave sectors (a trying state),may have granted control of its antenna resources to another mastersector (a hold state), may have already acquired control of the slavesectors and may be performing the optimization procedure (an activestate), may have finished the optimization procedure and be releasingantenna resources (an exit state), or may be idle (an idle state). Thepotential master sectors 305 may also be associated with other variables345 such as a “hold” variable or a “request” variable. In thephilosopher's dining problem 330, each master sector 305 may also beassociated with a node in a precedence graph 350 that indicates therelative precedence of each master sector 305 with respect to otherneighboring sectors. As discussed herein, each potential master sector305 may also determine whether to grant or deny a request for theantenna resources 335 based in part on its current state.

Negotiating the allocation of master sectors and slave sectors on thebasis of grants or requests that may be granted or denied on the basisof the relative precedence of the sectors and the current state of thesectors has a number of advantages over conventional practice. Forexample, this approach is well-suited for implementing parallel(concurrent) allocation of the master and slave sectors. Furthermore,there are mathematical proofs of the existence of solutions to idealizedversions of the philosopher's problem.

In one embodiment, the mapping 300 may be used to support optimizationof antenna tilts in a radio access system. For example, one sector maybe selected as a master sector and optimization functionality in themaster sector may optimize its own tilt and the tilt of some closeneighbors (e.g., slave sectors). A further ring of sectors may be formedaround the slave sectors. The sectors in the further ring may not changetheir tilts during the optimization, but these sectors may besufficiently close to the master sector or the slave sectors to feel theeffect of the tilt changes. Further outside are sectors that areregarded as substantially unaffected because they are sufficiently farfrom the master and slave sectors. The master sector, the slave sectors,and the affected ring of sectors may make performance measurements togive indications about the performance of this region. Grantingexclusive control of the resources to the master sector during theallocation process may allow the optimization functionality to establisha clean cause-to-effect function (e.g., performance figures derived fromthe measurements as a function of the various multiple tilt settingcombinations). The activities of the optimization functionality in themaster sectors should therefore be sufficiently decorrelated. Allowingmultiple optimization centers in multiple master sectors to control thesame slave sectors may disturb the performance measurements and mayreduce the precision of the optimization algorithm. The radio system isassumed to be in operational mode during the optimization process and sothe test changes should be small enough that they have a detectableeffect, but not a significant negative effect on the performance andcoverage as experienced by the user of the mobile terminals. Thisapproach does not require either a tilt-prediction model or planningdata at least in part because it is based on the observed performancemeasurements and can adapt itself automatically to environmental changeswithout manual intervention.

FIG. 4 conceptually illustrates a second exemplary embodiment of awireless communication system 400. In the illustrated embodiment, thewireless communication system whose one or more base stations 405, 407for providing uplink/downlink wireless connectivity to one or more userequipment 410. The base station 405 is electromagnetically and/orcommunicatively coupled to an active antenna array 415 that includesmultiple antennas 420 for transmitting downlink signals to the userequipment 410 and receiving uplink signals from the user equipment 410.A transceiver (RX/TX) 425 in the base station 405 is used to generatesignals and provide the signals to the antenna array 415 to drive thedownlink transmissions. The transceiver 425 may also be configured toreceive uplink signals from the antenna array 415. In some embodiments,the base station 407 may be configured in a similar manner to the basestation 405 or it may use a different configuration. In the interest ofclarity the detailed configuration of the base station 407 is notdepicted in FIG. 4.

The illustrated embodiment of the base station 400 includes an optimizer430 that may be configured to optimize antenna resources for one or moresectors that are served by the base station 400 using the antenna array415 and one or more slave sectors when the base station 400 is providingcoverage to a master sector, as discussed herein. The optimizer 430 mayalso be configured to receive instructions from other base stations anduse these instructions to implement optimizations of the antennaresources associated with the antenna array 415 when the base station405 is operating as a slave sector.

The base station 400 may also be configured to make performancemeasurements using performance measurement functionality 435. Exemplaryperformance measurements include, but are not limited to, measuringblock error rates for uplink transmissions, channel quality for uplinkchannels, or other measures of the coverage or capacity supported by thebase station 405. The performance measurement functionality 435 may alsobe configured to receive information indicating the results ofperformance measurements performed by other entities such as a basestation 407 and user equipment 410.

In the illustrated embodiment, the base station 400 can use informationacquired from user equipment 410 and communication with other basestations 407 to identify neighboring sectors using neighborhood analysisfunctionality 437. Neighborhood measurements performed by user equipment410 and subsequent signaling with near and far neighbors(neighbor-of-neighbor . . . ) of the neighboring sectors identified bythe user equipment can be used to build a local view of the distributedgraph (e.g., the nodes and plain arcs), as discussed herein. In oneembodiment, the local view may include free nodes, which might bequeried by other sectors that are attempting to identify theirneighbors. Negotiations between neighboring sectors may be performedusing functionality in the performance measurement element 437. Forexample, the performance measurement elements 437 may perform orparticipate in negotiations that are used to determine who is next to bemaster or slave, when the change graph arc directions, how to set statusbits, or how to decide the roles for each sector.

User equipment 410 includes a transceiver 440 that may be configured totransmit uplink signals towards the base stations 405, 407 or to receivedownlink signals from the base stations 405, 407. User equipment 410 mayalso be configured to make performance measurements using functionality445. Exemplary performance measurements include, but are not limited to,measuring block error rates for downlink transmissions, channel qualityinformation or pre-coding matrix information for downlink channels, orother measures of the coverage or capacity supported by the base station405. In the illustrated embodiment, information indicative of theperformance measurements may be fed back to the base station 405 so thatit can be used as part of the antenna optimization process describedherein. In one embodiment, the base station 407 may be configured tomake performance measurements and feed information indicating theresults of the performance measurements back to the base station 405 sothat these results may be used as part of the antenna optimizationprocess.

FIG. 5 conceptually illustrates one exemplary embodiment of a method 500for coordinating concurrent sector optimization at a wirelesscommunication system. In the illustrated embodiment, the wirelesscommunication system includes a plurality of base stations that serve acorresponding number of sectors. Neighbor relationships between thesectors can be determined (at 505) using performance measurements thatmay be performed by the various base stations, sectors, or userequipment in the wireless communication system. The neighborrelationships may be used to construct (at 510) a precedence graph thatindicates the relative precedence of each sector to its neighbor. In oneembodiment, the precedence graph can be initialized by giving eachsector a unique start identifier, for which a comparison operator like“greater than” is defined to determine the relative precedence. Forexample, the nodes in the precedence graph associated with each sectorcan be assigned a random number or another unique identifier such as anumber determined by concatenating the boot time of a base station withthe serial number of the base station or a sector identifier. The uniqueidentifier may therefore be calculated locally (e.g., by the basestation) without checking for duplicates even if the base station'sclock is slightly wrong. A new number may be calculated following asystem or base station crash to avoid confusion caused by messages thatmay be circulating around the system and which may still be identifiedby the pre-crash identifier. The pre-crash identifiers may therefore beremoved from the memory of the system. In one embodiment, the precedencegraph may be constructed (at 510) and stored in a centralized locationor database. However, persons of ordinary skill in the art havingbenefit of the present disclosure should appreciate that the method 500is not limited to embodiment that implements a centralized database.Alternative embodiments may implement distributed databases for storingportions of the precedence graph in different locations, e.g., a portionof the precedence graph may be stored in a location or databaseassociated with each sector.

FIG. 6A conceptually illustrates a portion 600 of a precedence graphthat may be used in embodiments of the techniques described herein. Inthe illustrated embodiment, the portion 600 of the precedence graphincludes a plurality of nodes 605 that are each associated with a sectorof the wireless communication system. Precedence between the nodes 605is indicated by directed arcs 610 between the various nodes 605. Higherprecedence is given to the nodes 605 when the corresponding directed arc610 points to the node 605 and lower precedence is giving to the nodes605 when the corresponding directed arc 610 points away from the node605. In the illustrated embodiment, the node 615 has a higher precedencethan all of its neighbor nodes 605 and so the node 615 may be selectedas a master sector for an iteration of the optimization process, asindicated by the bold circle. However, alternative indications of therelative precedence of the nodes 605, 615 may be used in alternativeembodiments.

Referring back to FIG. 5, the method 500 may use an iteration counter(i) to determine when to terminate iterations of the optimizationprocess. In the illustrated embodiment, the iteration counter isincremented (at 515) before iterations of the optimization process andthe process can continue until the iteration counter reaches apredetermined value (N). However, persons of ordinary skill in the arthaving benefit of the present disclosure should appreciate thatalternative stopping criteria may be used in different embodiments ofthe method 500. In one alternative embodiment, the method 500 maycontinue to iterate until a convergence criterion is satisfied. Forexample, the method may continue to iterate until the fractional changeper iteration in the values of the antenna parameters subject to theoptimization falls below a threshold value such as 1%.

For each iteration, one or more master sectors may be selected (at 520)for concurrent optimization along with the corresponding slave sectors.In one embodiment, the master sector and slave sectors may be selected(at 520) according to embodiments of the techniques described herein,such as the techniques depicted in FIGS. 1-3. In one embodiment, themaster sectors may be selected (at 520) concurrently with selection ofother master sectors. However, persons of ordinary skill in the arthaving benefit of the present disclosure should appreciate that themethod 500 is not limited to concurrent selection (at 520) of the mastersectors. Alternative embodiments of the method may allow each mastersector to be selected (at 520) independently or asynchronously withselection (at 520) of other master sectors. For example, one mastersector may attempt to acquire control of the neighbor resources bynegotiating with the others, which might at this time already be amaster sector, a slave sector, or a free sector. In alternativeembodiments, the i-loop (from 510 to 535) may therefore runindependently or asynchronously for each potential master sector.

The antenna resources for the master sector(s) and corresponding slavesectors may then be concurrently optimized (at 525). In one embodiment,a gradient ascent method may be used to perform the optimization foreach master sector and its associated slave sectors. For example, avariation of the gradient ascent method may be used to optimize thevertical antenna tilt of an orthogonal frequency division multipleaccess (OFDMA) base station with respect to a given utility metric. Inthe illustrated embodiment, each base station provides coverage to acell that is divided up into three sectors and the overall systemtopology consists of a set P of sectors with a total of |P| antennas for|P| sectors. An exemplary utility metric may be defined as:

$\mspace{20mu}{U = {\frac{1}{P}\left( {{W_{avg}s_{m,{avg}}} + {W_{edge}s_{m,{edge}}}} \right)}}$In this utility metric, the average spectral efficiency over the entiresector m is given by s_(m,avg) and the 5% quantile of the distributionof the spectral efficiency over the entire sector m is given bys_(m,edge). One set of exemplary weights is given by:

$W_{avg} = {{\frac{1}{{{bits}/s}/{Hz}}\mspace{14mu}{and}\mspace{14mu} W_{edge}} = \frac{10}{{{bits}/s}/{Hz}}}$However, persons of ordinary skill in the art having benefit of thepresent disclosure should appreciate that the values of the weights arematters of design choice.

In the illustrated embodiment, each antenna mεP can adopt an individualtilt so that the tilt of all the antennas can be described as a tiltvector:

$\mspace{20mu}{\overset{\_}{\varphi} = \begin{pmatrix} \\\varphi_{m} \\

\end{pmatrix}}$The tilt vector has |P| dimensions. In the illustrated embodiment, theangles of the tilt can be initialized to a predetermined value such as11°. The master sector (j_(t)) is chosen as a starting point and theslave sectors are combined with the master sector to form a cluster:C _(j) ={j _(i) }∪{m|m=neighbor(j _(i))}As discussed herein, the slave sectors for each master sector may beidentified using neighbor relations that may be determined usingperformance measurements such as measurements of mutual interferencebetween sectors. Within the set of sectors C_(j), the gradient of theutility function U with respect to the individual tilt φ_(i) can bedetermined using the individual differentials:

$\mspace{20mu}{\frac{\partial U}{\partial\varphi_{i}} = \left\{ {{\begin{matrix}\frac{{U\left( {\varphi_{i} + \Delta_{i}} \right)} - {U\left( {\varphi_{i} - \Delta_{i}} \right)}}{\left( {\varphi_{i} + \Delta} \right) - \left( {\varphi_{i} - \Delta} \right)} & {{{for}\mspace{14mu} t} \in {C_{j}\backslash S}} \\0 & {else}\end{matrix}\mspace{20mu}{where}\mspace{20mu}\Delta_{i}} = \begin{pmatrix} \\{\Delta_{\bullet}\delta_{im}} \\

\end{pmatrix}} \right.}$for mεP and δ_(im) is the Kronecker delta function. The set S is definedas:S={i|U _((φ) _(j) ₎ <U _((φ) _(i) _(+Δ) _(i) ₎ and U _((φ) _(i) ₎ <U_((φ) _(i) _(−Δ) _(i) ₎}The set S is the set of sectors for which a change of the tilt angle byΔ_(i) in either direction indicates a minimum. The maximal absolutevalue of the tilt differentials is given by:

$\mspace{20mu}{= {\frac{\partial U}{\partial\varphi_{i}}}}$This maximal absolute value can be used as a normalization factor whendetermining the candidate vertical angles, e.g., using the followingexpression:

$\mspace{20mu}{\varphi_{m,k} = \left\{ \begin{matrix}\left\lfloor {\varphi_{m} + {\frac{\partial U}{\partial\varphi_{m}}} + 0.5} \right\rfloor & {{for}\mspace{14mu} mC_{j}\mspace{14mu}{and}\mspace{14mu} kK} \\\varphi_{m} & {{for}\mspace{14mu} m{P\backslash C_{j}}\mspace{14mu}{and}\mspace{14mu} kK}\end{matrix} \right.}$In the above expression, K={1, 2, . . . k_(max)}. The original set K isfurther modified to a set K* containing additional real number elementsthat are intermediate between the ones yielding the best and the secondbest utilities. In that case, a number |K*| of new tilt vectors, whichare indexed by k, can be obtained:

$\mspace{20mu}{\varphi_{k} = {\begin{pmatrix} \\\varphi_{m,k} \\

\end{pmatrix}\mspace{14mu}{for}\mspace{14mu}{all}\mspace{14mu} mP\mspace{14mu}{and}\mspace{14mu} kK^{*}}}$In this embodiment, the normalization factor c helps to limit thelargest change of an individual angle to ±k_(max).

The best-performing tilt vector may then be selected out of the testedangles:φ:φ_(i),φ_(l)+Δ_(i),φ_(i)−Δ_(i),φ_(k)The selected best-performing tilt vector can be adopted as the new tiltvector for the corresponding sector:

$\overset{\rightharpoonup}{\varphi_{i + 1}} = {\arg\;{\max\limits_{\varphi}\left( {U_{({\varphi\;}_{i})},\left\{ {U_{({\varphi_{i} + \Delta_{i}})}❘{i \in C_{j}}} \right\},\left\{ {U_{({\varphi_{i} - \Delta_{i}})}❘{i \in C_{j}}} \right\},\left\{ {U_{(\varphi_{i})}❘{k \in K^{*}}} \right\}} \right)}}$However, persons of ordinary skill in the art having benefit of thepresent disclosure should appreciate that alternative embodiments of themethod 500 may use other techniques for concurrently optimizing (at 525)the resources of the master and slave sectors. Moreover, optimization(at 525) of the antenna resources may include optimization of otherantenna parameters such as an azimuth, a transmission power, abeamforming parameter, or a beamwidth.

As each master sector completes the optimization (at 525), theprecedence arcs connected to the master and slave sectors involved inthe optimization may be reversed (at 530) so that the master sectorrelinquishes precedence to the neighbors at the other ends of the arcs.Reversing (at 530) precedence upon completion of the optimizationprocedure contributes to fairness of the method 500. The value of theiteration counter (i) may then be checked (at 535) to determine whetherthe stopping criterion (i>N) has been satisfied. If not, the iterationcounter is incremented (at 515) and another iteration of theoptimization process may be performed. If the stopping criterion issatisfied, the method 500 may end (at 540). Persons of ordinary skill inthe art having benefit of the present disclosure should appreciate thatthe stopping criterion shown in FIG. 5 is intended to be illustrative.Alternative embodiments of the method 500 may implement other stoppingcriteria. For example, the method 500 may iterate until a performancelimit is reached or until the gain per iteration becomes too small to beworth continuing. Furthermore, in some embodiments the method 500 maynot include a stopping criterion the method 500 may continue to iteratewithout limit.

FIG. 6B conceptually illustrates the portion 600 of a precedence graphfollowing iteration of the optimization process performed on the portion600 depicted in FIG. 6A. As discussed herein, precedence between thenodes 605 is indicated by directed arcs 610 between the various nodes605. Higher precedence is given to the nodes 605 when the correspondingdirected arc 610 points to the node 605 and lower precedence is given tothe nodes 605 when the corresponding directed are 610 points away fromthe node 605. However, the precedence indicated by the directed arcs 600connected to the node 615 in FIG. 6B has been reversed relative to theorientation of the corresponding directed arcs 610 shown in FIG. 6A. Inthe illustrated embodiment, the node 615 now has a lower precedencerelative to its neighbor nodes 605. A different node 620 now has higherprecedence relative to its neighbor nodes 605 and may be selected as amaster sector for an iteration of the optimization process, as indicatedby the bold circle.

FIG. 7 conceptually illustrates one exemplary embodiment of the result700 of the simulation that implements embodiments of the sectorselection and optimization process described herein. In the illustratedembodiment, sectors were simulated using an LTE downlink radio model.The 19 site locations are randomly displaced from regular positions andslow fading was assumed for the downlink transmissions. A 3-D antennamodel was used. The optimization metric included capacity and coverageand was optimized over the whole area depicted in FIG. 7. For historicreasons, the 57 sectors shown in FIG. 7 are numbered from 3 to 59. Thesimulation covers the area served by one optimization center (mastersector) and its neighbors (slave sectors) and periodic boundaryconditions are adopted so that the simulation area wraps around at theboundaries. In the illustrated embodiment, the optimization centercoordinates its own antenna tilt and the tilt changes of its 6 closestneighbors. The remaining 50 sectors keep their antenna tilt unchanged,but they may be affected by interference from the seven sectors that areparticipating in the optimization and each of the sectors makesperformance measurements. No unaffected sectors are shown. FIG. 7depicts the coverage areas of the sectors after the optimization hascompleted. In the illustrated embodiment, the optimization procedure wasiterated so that each of the 57 sectors acted as the optimization centerfor several iterations until a stable overall performance equilibriumwas achieved.

FIG. 8 conceptually illustrates one exemplary embodiment of a server 800that may be used to determine or store neighbor lists for sectors of awireless communication system, define or store precedence graphs basedon the neighbor list, or perform concurrent sector optimizations. In theillustrated embodiment, the server 800 includes a processor 805, datastorage 810, and an input/output (I/O) interface 815. The processor 805is configured to control operation of the server 800. e.g., using dataor instructions stored in the data storage 810 or at other locations.Embodiments of the operations that may be performed by the server 800are described herein in conjunction with FIGS. 1-7. In one embodiment,the data storage 810 stores information 820 that represents one or moresector neighbor lists, information 825 that represents portions of theprecedence graph, or information 830 that represents antenna resourcesduring intermediate stages of concurrent optimization or followingcompletion of concurrent optimization.

Although FIG. 8 depicts a single server 800, persons of ordinary skillin the art having benefit of the present disclosure should appreciatethat alternative embodiments may use multiple servers and may distributeportions of the functionality depicted FIG. 8 throughout the multipleservers. In some embodiments, the server 800 may be a virtual machine.In some of these embodiments, the virtual machine may include componentsfrom different machines or be geographically dispersed. For example, thedata storage 810 and the processor 805 may be in two different physicalmachines. In one embodiment, the server 800 may be implemented as adistributed server that is incorporated in multiple base stations(serving numerous sectors) without the need for a central server. Whenprocessor-executable programs such as the social network services 830are implemented on the processor 805, the program code segments combinewith the processor 805 to provide a unique device that operatesanalogously to specific logic circuits.

Portions of the disclosed subject matter and corresponding detaileddescription are presented in terms of software, or algorithms andsymbolic representations of operations on data bits within a computermemory. These descriptions and representations are the ones by whichthose of ordinary skill in the art effectively convey the substance oftheir work to others of ordinary skill in the art. An algorithm, as theterm is used here, and as it is used generally, is conceived to be aself-consistent sequence of steps leading to a desired result. The stepsare those requiring physical manipulations of physical quantities.Usually, though not necessarily, these quantities take the form ofoptical, electrical, or magnetic signals capable of being stored,transferred, combined, compared, and otherwise manipulated. It hasproven convenient at times, principally for reasons of common usage, torefer to these signals as bits, values, elements, symbols, characters,terms, numbers, or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise, or as is apparent from the discussion,terms such as “processing” or “computing” or “calculating” or“determining” or “displaying” or the like, refer to the action andprocesses of a computer system, or similar electronic computing device,that manipulates and transforms data represented as physical, electronicquantities within the computer system's registers and memories intoother data similarly represented as physical quantities within thecomputer system memories or registers or other such information storage,transmission or display devices.

Note also that the software implemented aspects of the disclosed subjectmatter are typically encoded on some form of program storage medium orimplemented over some type of transmission medium. The program storagemedium may be magnetic (e.g., a floppy disk or a hard drive) or optical(e.g., a compact disk read only memory, or “CD ROM”), and may be readonly or random access. Similarly, the transmission medium may be twistedwire pairs, coaxial cable, optical fiber, or some other suitabletransmission medium known to the art. The disclosed subject matter isnot limited by these aspects of any given implementation.

The particular embodiments disclosed above are illustrative only, as thedisclosed subject matter may be modified and practiced in different butequivalent manners apparent to those skilled in the art having thebenefit of the teachings herein. Furthermore, no limitations areintended to the details of construction or design herein shown, otherthan as described in the claims below. It is therefore evident that theparticular embodiments disclosed above may be altered or modified andall such variations are considered within the scope of the disclosedsubject matter. Accordingly, the protection sought herein is as setforth in the claims below.

What is claimed:
 1. A method, comprising: determining, in at least oneserver, neighbor relationships between a plurality of sectors;constructing, in the at least one server, a precedence graph using theneighbor relationships to link neighboring sectors by a plurality ofdirected arcs to indicate relative precedence of the neighboringsectors; and iteratively allocating, in the at least one server, atleast one antenna resource of each of the plurality of sectors by:selecting a subset of the plurality of sectors as master sectors,wherein each master sector is associated with at least one slave sectorthat neighbors the master sector, and wherein each master sector hasprecedence over its associated slave sectors, and wherein each slavesector is only associated with one master sector; concurrentlyoptimizing allocation of said at least one antenna resource for eachmaster sector and its associated slave sectors; reversing precedenceindicated by the directed arcs linked to each master sector followingoptimization of the allocation of said at least one antenna resource;and iterating so that each of the plurality of sectors is selected as amaster sector for at least one iteration.
 2. The method of claim 1,wherein said at least one antenna resource comprises at least one of anantenna tilt, an azimuth, a transmission power, a beamforming parameter,or a beamwidth.
 3. The method of claim 1, wherein determining theneighbor relationships comprises determining the neighbor relationshipsbased on inter-sector interference levels that are determined based onperformance measurements that indicate radiation patterns of each of theplurality of sectors.
 4. The method of claim 3, wherein determining theneighbor relationships comprises determining the neighbor relationshipsbased on performance measurements made by at least one of the pluralityof sectors or at least one user equipment served by at least one of theplurality of sectors.
 5. The method of claim 1, wherein determining theneighbor relationships comprises receiving reports from user equipmentidentifying other sectors detected by the user equipment and thencommunicating with said other sectors to identify at least oneadditional neighboring sector.
 6. The method of claim 1, whereinselecting the master sectors comprises exchanging a request to become amaster sector between neighboring sectors and determining whether togrant the request based on a directed arc between the neighboringsectors and a state of the sector that receives the request.
 7. Themethod of claim 6, wherein the state of the sector comprises at leastone of optimizing, attempting to optimize, holding for optimization, oridle.
 8. A method comprising: selecting, in at least one server, asubset of a plurality of sectors as master sectors, wherein each mastersector is associated with at least one slave sector that neighbors themaster sector, and wherein each master sector has precedence over itsassociated slave sectors, and wherein each slave sector is onlyassociated with one master sector; optimizing, in the at least oneserver, allocation of at least one antenna resource of each mastersector concurrently with antenna resources of its associated slavesectors; selecting, in the at least one server, a new subset of mastersectors by reversing precedence between master sectors and theirassociated slave sectors following optimization of the allocation ofsaid at least one antenna resource; and iterating so that each of theplurality of sectors is selected by the at least one server as a mastersector for at least one iteration.
 9. The method of claim 8, whereinsaid at least one antenna resource comprises at least one of an antennatilt, an azimuth, a transmission power, a beamforming parameter, or abeamwidth.
 10. The method of claim 8, further comprising: determiningneighbor relationships between the plurality of sectors; andconstructing a precedence graph using the neighbor relationships to linkneighboring sectors by a plurality of directed arcs to indicate relativeprecedence of the neighboring sectors.
 11. The method of claim 10,wherein determining the neighbor relationships comprises determining theneighbor relationships based on inter-sector interference levels thatare determined based on performance measurements that indicate radiationpatterns of each of the plurality of sectors.
 12. The method of claim11, wherein determining the neighbor relationships comprises determiningthe neighbor relationships based on performance measurements made by atleast one of the plurality of sectors or at least one user equipmentserved by at least one of the plurality of sectors.
 13. The method ofclaim 10, wherein determining the neighbor relationships comprisesreceiving reports from user equipment identifying other sectors detectedby the user equipment and then communicating with said other sectors toidentify at least one additional neighboring sector.
 14. The method ofclaim 8, wherein selecting the master sectors comprises exchanging arequest to become a master sector between neighboring sectors anddetermining whether to grant the request based on a directed arc betweenthe neighboring sectors and a state of the sector that receives therequest.
 15. The method of claim 14, wherein the state of the sectorcomprises at least one of optimizing, attempting to optimize, holdingfor optimization, or idle.